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Intrebare

 
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Beniamin Bogosel
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Joined: 07 Mar 2008
Posts: 760
Location: Chambery, Franta

PostPosted: Tue Jun 08, 2010 8:17 pm    Post subject: Intrebare Reply with quote

Daca avem un operator marginit si injectiv T:X \to X astfel incat T y_n \to 0 atunci ce putem spune despre sirul y_n? Tinde la 0, are un subsir care tinde la 0?
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Dragos Fratila
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Joined: 04 Oct 2007
Posts: 335
Location: Paris

PostPosted: Wed Jun 09, 2010 8:08 pm    Post subject: Reply with quote

Considera un spatiu Hilbert cu o baza ortonormata e_i, i\in\mathbb{N} si operatorul T definit prin T(e_n) = \frac{e_n}n.
E clar ca e marginit, injectiv si T(e_n)\to 0 dar sirul \{e_n\}_n n-are pe 0 ca punct de acumulare.
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